Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Let R be the set of real numbers, f : R?R be the function defined by f (x) = 4x + 3, x ? R. Show that f is invertible. Find the inverse of f ?

Let R be the set of real numbers, f : R?R be the function defined by f (x) = 4x + 3, x ? R. Show that f is invertible. Find the inverse of f ?

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
f : R\rightarrow R
f(x) = 4x + 3
Since range of function is equal to co-domain, so it is onto function.
It is straight line, so it is clear from the graph that it is one to one function.
-> f(x) is bijective function, so it can be invertible.
x\rightarrow f^{-1}(x)
f(f^{-1}(x)) = 4f^{-1}(x) + 3
f(f^{-1}(x)) = x
f^{-1}(x) = \frac{x-3}{4}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free